distributed optimization of fiber optic network layout ...uhl/iccsa_slides.pdf · 2. the...

School of Telematics & Network Engineering http://www.cti.ac.at/

Distributed Optimization of Fiber Optic Network Layoutusing MATLAB

R. Pfarrhofer, M. Kelz, P. Bachhiesl, H. Stogner, and A. [email protected]

R. Pfarrhofer, M. Kelz, P. Bachhiesl, H. Stogner, and A. Uhl 1 Carinthia Tech Institute & Salzburg University


Outline

• Introduction

• MATLAB Custer Computing: MDICE

• Optimization of Fiber Optic Network Layout

– Sequential Approach– Distribution Strategy– Experimental Results

• Conclusions



Introduction

• About 95% of the total costs for the implementation of fiber optic networksmay be expected for the area-wide realization of the last mile (access networks)– planning tools currently are employed for the core net domain only.

• NETQUEST-OPT is a MATLAB-based planning tool for the computation ofcost optimized and real world laying for fiber optic access networks, it is basedon cluster strategies, exact and approximative graph theoretical algorithms,combinatorial optimization, and ring closure heuristics.

• NETQUEST-OPT currently requires computation times of several hours on asingle workstation even for medium sized access domains.

• For an efficient planning process interactivity is a desired property, e.g. for rapidprototyping of different clustering strategies → high performance computingsystems are required.



Cluster Computing and MATLAB

• Emerge of cluster computing → a cheap and highly available and yet powerfularchitecture for image processing applications

• MATLAB provides users with easy access to an extensive library of high qualitynumerical routines which can be used in a dynamical way and may be easilyextended and integrated into existing applications.

• MATLAB in HPC

– Developing a high performance interpreter (MPI/PVM based communicationroutines) or coarse grained parallelization by splitting up work among multipleMATLAB sessions.

– Calling high performance numerical libraries (e.g. SCALAPACK)– Compiling MATLAB to another language (e.g. C, HPF)



MDICE

• MDICE: MATLAB-based DIstributed Computing Environment

• Goal: in contrast to previous approaches the goal is to get along with a singleMATLAB client (instead of a MATLAB client at each participating computenode)

• The main idea was to change the client program in a way that it can becompiled to a standalone application.

• The compiled client program library and the datasets for the job are sent to thecompute node, where a background client service is running with low priority.

• For this reason the involved client machines may be used as desktop machinesby other users during the computation.



Client-Server Concept of MDICE

Downloadhttp://www.fh-kaernten.at/nocms/studiengaenge/ma-tel/mdice/



Optimization of Fiber Optic Network Layout: Sequential I

• We map the real world geometriesto a set of nodes V of a graphG = (V,E).

• Penalty Grid: A spatially balancedscore card combines all relevant landclasses with typical implementationcosts. The access net domain isregarded as a regular grid [xi, xi+1]×[yj, yj+1], i and j are indices offinite index sets. Each entry ofthe penalty matrix P describes thespecific implementation costs for thegrid pixel [xi,xi+1]× [yj, yj+1].



Optimization of Fiber Optic Network Layout: Sequential II

• For an edge [u, v], u ∈ V , v ∈V , u 6= v, we define the entry

Wu,v of the symmetric cost matrix

W ∈ Mat (|V | × |V |) according to

Wu,v :=∑K−1

k=0 ‖sk+1 − sk‖2 Pk+1.• The computation of W is one of the

most time demanding procedures in

the entire laying optimization process

and requires (|V | − 1) |V | /2 calls of

computing Wu,v.

• In real world geometries, the network

planning problem leads to dimensions up

to |V | ∼= 20000 nodes, therefore we

first determine local clusters, compute a

local solution in each cluster and find

cluster shortest spanning trees.



Optimization of Fiber Optic Network Layout: Sequential III

easting [m]

nort

hing

[m]

C(1)

C(2)

C(3)

69 269 469 669 869 1069 1269

77

277

477

677

877

1077

1277

1477

1677

37 access nodes (triangles) Arial view of target areaand three clusters (with overlayed computed solution)



Optimization of Network Layout: Distribution Strategy• Inter-cluster approach: parallelization by segmentation of the spatial domain

into independent clusters is efficient but leads to suboptimal global umbrellanetworks only, especially in case of a larger number of clusters which would berequired for scalable parallel or distributed execution.

• Intra-cluster approach: does not exploit the parallelism introduced by theclustering process at all, therefore an optimal global solution may be obtainedif clustering can be avoided. In this context, the computations associated withthe evaluation of the cost matrix W (which are covered by our experiments)may be distributed in a simple fashion by domain decomposition without therequirement of inter-process communication.

This simple partitioning approach leads to entirely deterministic behaviour sincethe computational effort of evaluating parts of the matrix W is not data dependent,however, load balancing functionalities are provided in order to be able to cope withthe possible interference of other applications and heterogeneous environments.



Experimental Settings• We consider cost matrices W from real-world problems associated with a

different number of edges (i.e. 36950, 114350, 394650, and 1227714) andvary the number of jobs distributed among the workers after fixing the edgesto 394650.

• Computational task is split into a certain number of equally sized jobs Nto be distributed by the server among the M clients in a dynamic fashion(“asynchronous single task pool method”)

• Server machine (1.99 GHz Intel Pentium 4, 504 MB RAM) and client machines(996 MHz Intel Pentium 3, 128 MB RAM and 730 MHz Intel Pentium 3, 128MB RAM), all types under Windows XP Prof., 100 MBit/s Ethernet network.

• Sequential reference times have been achieved on a 996 MHz client machinewith a compiled (not interpreted) version of the application to allow a faircomparison

• We use MATLAB 6.5.0 with the MATLAB compiler 3.0 and the LCC Ccompiler 2.4.

• Homogenous environment (fast clients only) vs. Heterogenous environment(six 996 MHz and four 730 MHz clients)



Experimental Results I: Homogenous Environment

• It is clearly exhibited that speedup saturates for the smaller problems at 4 or 8 clients,

respectively. On the other hand, reasonable scalability is shown for the larger problems up to

20 clients.

• The number of clients is set to 10, and 30 jobs are used. The staggered start of computation

at different clients which is due to the expensive initial communication phase.

2 4 6 8 10 12 14 16 18 20

2

4

6

8

10

12

14

16

Number of worker−nodes

Spe

edup

36,950 edges (25 jobs) 114,350 edges (25 jobs) 394,650 edges (25 jobs)1,227,714 edges (73 jobs)

0 100 200 300 400 500 600

1

2

3

4

5

6

7

8

9

10

Time in secondsW

orke

r

Doing nothingCommunicatingProcessing

Speedup for varying problem-size Visualization of execution



Experimental Results II: Heterogenous Environment• We vary the number of jobs distributed among the clients. Clearly, a high number of jobs leads

to an excellent load distribution, but on the other hand the communication effort is increased

thereby reducing the overall efficiency. The optimal number of jobs is identified to be 75.• With 10 jobs on 10 clients, the performance is worse as compared to the analogous homogenous

case and the slower clients (numbers 3,6,7,8) are immediately identified.

10 15 18 25 30 45 50 75 90 150 225700

750

800

850

900

950

1000

Number of jobs

Tim

e in

sec

onds

0 100 200 300 400 500 600 700 800

1

2

3

4

5

6

7

8

9

10

Time in secondsW

orke

r


Execution time Visualization of execution(varying number of jobs) (10 jobs)



Experimental Results III: Execution Visualization

• Execution behaviour for 25 and 75 jobs: visual appearance of the two cases is quite different,

but we result in almost identical execution times.

• Whereas for N = 25 we have little communication effort but highly unbalanced load, the

opposite is true for N = 75.

0 100 200 300 400 500 600 700

1

2

3

4

5

6

7

8

9

10

Time in seconds

Wor

ker


0 100 200 300 400 500 600 700

1

2

3

4

5

6

7

8

9

10

Time in seconds

Wor

ker


25 Jobs 75 Jobs



Conclusions

1. The custom MATLAB toolbox MDICE may take advantage of the largenumber of Windows NT-architecture based machines available in companiesand universities at low licensing costs.

2. The distributed approach suggested in this work allows for an interactivenetwork planning process provided enough PCs are available.

3. Additionally, our approach may lead to a better quality of the computednetwork solution as compared to a sequential clustering approach in case theclustering can be avoided in the distributed execution.


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